AbstractFeObjectAssembler.hpp

/*

Copyright (C) University of Oxford, 2005-2011

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#ifndef ABSTRACTFEOBJECTASSEMBLER_HPP_
#define ABSTRACTFEOBJECTASSEMBLER_HPP_

#include "LinearBasisFunction.hpp"
#include "GaussianQuadratureRule.hpp"
#include "BoundaryConditionsContainer.hpp"
#include "ReplicatableVector.hpp"
#include "DistributedVector.hpp"
#include "HeartEventHandler.hpp"
#include "AbstractTetrahedralMesh.hpp"
#include "PetscTools.hpp"

typedef enum InterpolationLevel_
{
    CARDIAC = 0,
    NORMAL,
    NONLINEAR
} InterpolationLevel;


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
class AbstractFeObjectAssembler : boost::noncopyable
{
protected:

    Vec mVectorToAssemble;

    Mat mMatrixToAssemble;

    bool mAssembleMatrix;

    bool mAssembleVector;
    
    bool mZeroVectorBeforeAssembly;

    bool mApplyNeummanBoundaryConditionsToVector;
    
    bool mOnlyAssembleOnSurfaceElements;
    
    PetscInt mOwnershipRangeLo;
    PetscInt mOwnershipRangeHi;

    GaussianQuadratureRule<ELEMENT_DIM>* mpQuadRule;

    GaussianQuadratureRule<ELEMENT_DIM-1>* mpSurfaceQuadRule;

    typedef LinearBasisFunction<ELEMENT_DIM> BasisFunction;
    typedef LinearBasisFunction<ELEMENT_DIM-1> SurfaceBasisFunction;


    ReplicatableVector mCurrentSolutionOrGuessReplicated;


    void ComputeTransformedBasisFunctionDerivatives(const ChastePoint<ELEMENT_DIM>& rPoint,
                                                    const c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian,
                                                    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rReturnValue);


    void DoAssemble();

    void ApplyNeummanBoundaryConditionsToVector();
    
    virtual double GetCurrentSolutionOrGuessValue(unsigned nodeIndex, unsigned indexOfUnknown)
    {
        return mCurrentSolutionOrGuessReplicated[ PROBLEM_DIM*nodeIndex + indexOfUnknown];
    }

protected:
    AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* mpMesh;

    BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* mpBoundaryConditions;

    virtual void ResetInterpolatedQuantities()
    {}

    virtual void IncrementInterpolatedQuantities(double phiI, const Node<SPACE_DIM>* pNode)
    {}    


    virtual c_matrix<double,PROBLEM_DIM*(ELEMENT_DIM+1),PROBLEM_DIM*(ELEMENT_DIM+1)> ComputeMatrixTerm(
        c_vector<double, ELEMENT_DIM+1>& rPhi,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double, PROBLEM_DIM, SPACE_DIM>& rGradU,
        Element<ELEMENT_DIM,SPACE_DIM>* pElement)
    {
        NEVER_REACHED;
        return zero_matrix<double>(PROBLEM_DIM*(ELEMENT_DIM+1),PROBLEM_DIM*(ELEMENT_DIM+1));
    }

    virtual c_vector<double,PROBLEM_DIM*(ELEMENT_DIM+1)> ComputeVectorTerm(
        c_vector<double, ELEMENT_DIM+1>& rPhi,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double, PROBLEM_DIM, SPACE_DIM>& rGradU,
        Element<ELEMENT_DIM,SPACE_DIM>* pElement)
    {
        NEVER_REACHED;
        return zero_vector<double>(PROBLEM_DIM*(ELEMENT_DIM+1));
    }

    virtual c_vector<double, PROBLEM_DIM*ELEMENT_DIM> ComputeVectorSurfaceTerm(
        const BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>& rSurfaceElement,
        c_vector<double, ELEMENT_DIM>& rPhi,
        ChastePoint<SPACE_DIM>& rX)
    {
        NEVER_REACHED;
        return zero_vector<double>(PROBLEM_DIM*ELEMENT_DIM);
    }
    
    virtual bool ElementAssemblyCriterion(Element<ELEMENT_DIM,SPACE_DIM>& rElement)
    {
        return true;
    }

    virtual void AssembleOnElement(Element<ELEMENT_DIM,SPACE_DIM>& rElement,
                                   c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1) >& rAElem,
                                   c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)>& rBElem);

    virtual void AssembleOnSurfaceElement(const BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>& rSurfaceElement,
                                          c_vector<double, PROBLEM_DIM*ELEMENT_DIM>& rBSurfElem);


public:
    AbstractFeObjectAssembler(AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh, unsigned numQuadPoints=2);

    void SetApplyNeummanBoundaryConditionsToVector(BoundaryConditionsContainer<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>* pBcc);

    void OnlyAssembleOnSurfaceElements(bool onlyAssembleOnSurfaceElements = true)
    {
        assert(CAN_ASSEMBLE_VECTOR);
        mOnlyAssembleOnSurfaceElements = onlyAssembleOnSurfaceElements;
    }
    
    void SetMatrixToAssemble(Mat& rMatToAssemble);

    void SetVectorToAssemble(Vec& rVecToAssemble, bool zeroVectorBeforeAssembly);

    void SetCurrentSolution(Vec currentSolution);


    void Assemble()
    {
        mAssembleMatrix = CAN_ASSEMBLE_MATRIX;
        mAssembleVector = CAN_ASSEMBLE_VECTOR;
        DoAssemble();
    }
        
    void AssembleMatrix()
    {
        assert(CAN_ASSEMBLE_MATRIX);
        mAssembleMatrix = true;
        mAssembleVector = false;
        DoAssemble();
    }

    void AssembleVector()
    {
        assert(CAN_ASSEMBLE_VECTOR);
        mAssembleMatrix = false;
        mAssembleVector = true;
        DoAssemble();
    }

    virtual ~AbstractFeObjectAssembler()
    {
        delete mpQuadRule;
        if(mpSurfaceQuadRule)
        {
            delete mpSurfaceQuadRule;
        }
    }
};






template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL> // class CONCRETE>
AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AbstractFeObjectAssembler(AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh, unsigned numQuadPoints)
    : mVectorToAssemble(NULL),
      mMatrixToAssemble(NULL),
      mZeroVectorBeforeAssembly(true),
      mApplyNeummanBoundaryConditionsToVector(false),
      mOnlyAssembleOnSurfaceElements(false),
      mpMesh(pMesh),
      mpBoundaryConditions(NULL)
{
    assert(pMesh);
    assert(numQuadPoints > 0);
    assert(CAN_ASSEMBLE_VECTOR || CAN_ASSEMBLE_MATRIX);

    mpQuadRule = new GaussianQuadratureRule<ELEMENT_DIM>(numQuadPoints);

    if(CAN_ASSEMBLE_VECTOR)
    {
        mpSurfaceQuadRule = new GaussianQuadratureRule<ELEMENT_DIM-1>(numQuadPoints);
    }
    else
    {
        mpSurfaceQuadRule = NULL;
    }
}  


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL> //, class CONCRETE>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::SetMatrixToAssemble(Mat& rMatToAssemble)
{
    assert(rMatToAssemble);
    MatGetOwnershipRange(rMatToAssemble, &mOwnershipRangeLo, &mOwnershipRangeHi);

    mMatrixToAssemble = rMatToAssemble;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL> //, class CONCRETE>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::SetVectorToAssemble(Vec& rVecToAssemble, bool zeroVectorBeforeAssembly)
{
    assert(rVecToAssemble);
    VecGetOwnershipRange(rVecToAssemble, &mOwnershipRangeLo, &mOwnershipRangeHi);

    mVectorToAssemble = rVecToAssemble;
    mZeroVectorBeforeAssembly = zeroVectorBeforeAssembly;
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL> //, class CONCRETE>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::SetCurrentSolution(Vec currentSolution)
{
    assert(currentSolution != NULL);
    // Replicate the current solution and store so can be used in
    // AssembleOnElement
    
    HeartEventHandler::BeginEvent(HeartEventHandler::COMMUNICATION);
    mCurrentSolutionOrGuessReplicated.ReplicatePetscVector(currentSolution);
    HeartEventHandler::EndEvent(HeartEventHandler::COMMUNICATION);
    
    // the AssembleOnElement type methods will determine if a current solution or
    // current guess exists by looking at the size of the replicated vector, so
    // check the size is zero if there isn't a current solution
    assert( mCurrentSolutionOrGuessReplicated.GetSize()>0 );
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL> //, class CONCRETE>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::DoAssemble()
{
    HeartEventHandler::EventType assemble_event;
    if (mAssembleMatrix)
    {
        assemble_event = HeartEventHandler::ASSEMBLE_SYSTEM;
    }
    else
    {
        assemble_event = HeartEventHandler::ASSEMBLE_RHS;
    }

    if(mAssembleMatrix && mMatrixToAssemble==NULL)
    {
        EXCEPTION("Matrix to be assembled has not been set");
    }
    if(mAssembleVector && mVectorToAssemble==NULL)
    {
        EXCEPTION("Vector to be assembled has not been set");
    }

    // this has to be below PrepareForAssembleSystem as in that
    // method the odes are solved in cardiac problems
    HeartEventHandler::BeginEvent(assemble_event);

    // Zero the matrix/vector if it is to be assembled
    if (mAssembleVector && mZeroVectorBeforeAssembly)
    {
        PetscVecTools::Zero(mVectorToAssemble);
    }
    if (mAssembleMatrix)
    {
        PetscMatTools::Zero(mMatrixToAssemble);
    }

    const size_t STENCIL_SIZE=PROBLEM_DIM*(ELEMENT_DIM+1);
    c_matrix<double, STENCIL_SIZE, STENCIL_SIZE> a_elem;
    c_vector<double, STENCIL_SIZE> b_elem;

    // loop over elements
    if(mAssembleMatrix || (mAssembleVector && !mOnlyAssembleOnSurfaceElements))
    {
        for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = mpMesh->GetElementIteratorBegin();
             iter != mpMesh->GetElementIteratorEnd();
             ++iter)
        {
            Element<ELEMENT_DIM, SPACE_DIM>& r_element = *iter;
    
            //Test for ownership first, since it's pointless to test the criterion on something which we might know nothing about.
            if ( r_element.GetOwnership() == true && ElementAssemblyCriterion(r_element)==true )
            {
                AssembleOnElement(r_element, a_elem, b_elem);
    
                unsigned p_indices[STENCIL_SIZE];
                r_element.GetStiffnessMatrixGlobalIndices(PROBLEM_DIM, p_indices);
    
                if (mAssembleMatrix)
                {
                    PetscMatTools::AddMultipleValues<STENCIL_SIZE>(mMatrixToAssemble, p_indices, a_elem);
                }
    
                if (mAssembleVector)
                {
                    PetscVecTools::AddMultipleValues<STENCIL_SIZE>(mVectorToAssemble, p_indices, b_elem);
                }
            }
        }
    }

    // Apply any Neumann boundary conditions
    //
    // NB. We assume that if an element has a boundary condition on any unknown there is a boundary condition
    // on unknown 0. This can be so for any problem by adding zero constant conditions where required
    // although this is a bit inefficient. Proper solution involves changing BCC to have a map of arrays
    // boundary conditions rather than an array of maps.


    if (mApplyNeummanBoundaryConditionsToVector && mAssembleVector)
    {
        HeartEventHandler::EndEvent(assemble_event);
        ApplyNeummanBoundaryConditionsToVector();
        HeartEventHandler::BeginEvent(assemble_event);
    }
    
    HeartEventHandler::EndEvent(assemble_event);
}


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::SetApplyNeummanBoundaryConditionsToVector(BoundaryConditionsContainer<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>* pBcc)
{
    assert(CAN_ASSEMBLE_VECTOR);
    mApplyNeummanBoundaryConditionsToVector = true;
    mpBoundaryConditions = pBcc;
}


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::ApplyNeummanBoundaryConditionsToVector()
{
    assert(mAssembleVector);
    assert(mpBoundaryConditions != NULL);
    
    HeartEventHandler::BeginEvent(HeartEventHandler::NEUMANN_BCS);
    if (mpBoundaryConditions->AnyNonZeroNeumannConditions())
    {
        typename BoundaryConditionsContainer<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>::NeumannMapIterator
            neumann_iterator = mpBoundaryConditions->BeginNeumann();
        c_vector<double, PROBLEM_DIM*ELEMENT_DIM> b_surf_elem;

        // Iterate over defined conditions
        while (neumann_iterator != mpBoundaryConditions->EndNeumann())
        {
            const BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>& r_surf_element = *(neumann_iterator->first);
            AssembleOnSurfaceElement(r_surf_element, b_surf_elem);

            const size_t STENCIL_SIZE=PROBLEM_DIM*ELEMENT_DIM; // problem_dim*num_nodes_on_surface_element
            unsigned p_indices[STENCIL_SIZE];
            r_surf_element.GetStiffnessMatrixGlobalIndices(PROBLEM_DIM, p_indices);
            PetscVecTools::AddMultipleValues<STENCIL_SIZE>(mVectorToAssemble, p_indices, b_surf_elem);
            ++neumann_iterator;
        }
    }
    HeartEventHandler::EndEvent(HeartEventHandler::NEUMANN_BCS);
}





// Implementation - AssembleOnElement and smaller


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::ComputeTransformedBasisFunctionDerivatives(
        const ChastePoint<ELEMENT_DIM>& rPoint,
        const c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rReturnValue)
{
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);
    static c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> grad_phi;

    LinearBasisFunction<ELEMENT_DIM>::ComputeBasisFunctionDerivatives(rPoint, grad_phi);
    rReturnValue = prod(trans(rInverseJacobian), grad_phi);
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AssembleOnElement(
    Element<ELEMENT_DIM,SPACE_DIM>& rElement,
    c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1) >& rAElem,
    c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)>& rBElem)
{
    c_matrix<double, SPACE_DIM, ELEMENT_DIM> jacobian;
    c_matrix<double, ELEMENT_DIM, SPACE_DIM> inverse_jacobian;
    double jacobian_determinant;

    mpMesh->GetInverseJacobianForElement(rElement.GetIndex(), jacobian, jacobian_determinant, inverse_jacobian);

    // With the new signature of GetInverseJacobianForElement, inverse and jacobian are returned at the same time
    //        // Initialise element contributions to zero
    //        if ( mAssembleMatrix || this->ProblemIsNonlinear() ) // don't need to construct grad_phi or grad_u in that case
    //        {
    //            this->mpMesh->GetInverseJacobianForElement(rElement.GetIndex(), inverse_jacobian);
    //        }

    if (mAssembleMatrix)
    {
        rAElem.clear();
    }

    if (mAssembleVector)
    {
        rBElem.clear();
    }

    const unsigned num_nodes = rElement.GetNumNodes();

    // allocate memory for the basis functions values and derivative values
    c_vector<double, ELEMENT_DIM+1> phi;
    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> grad_phi;

    // loop over Gauss points
    for (unsigned quad_index=0; quad_index < mpQuadRule->GetNumQuadPoints(); quad_index++)
    {
        const ChastePoint<ELEMENT_DIM>& quad_point = mpQuadRule->rGetQuadPoint(quad_index);

        BasisFunction::ComputeBasisFunctions(quad_point, phi);

        if ( mAssembleMatrix || INTERPOLATION_LEVEL==NONLINEAR )
        {
            ComputeTransformedBasisFunctionDerivatives(quad_point, inverse_jacobian, grad_phi);
        }

        // Location of the gauss point in the original element will be stored in x
        // Where applicable, u will be set to the value of the current solution at x
        ChastePoint<SPACE_DIM> x(0,0,0);

        c_vector<double,PROBLEM_DIM> u = zero_vector<double>(PROBLEM_DIM);
        c_matrix<double,PROBLEM_DIM,SPACE_DIM> grad_u = zero_matrix<double>(PROBLEM_DIM,SPACE_DIM);

        // allow the concrete version of the assembler to interpolate any
        // desired quantities
        ResetInterpolatedQuantities();

        // interpolation
        for (unsigned i=0; i<num_nodes; i++)
        {
            const Node<SPACE_DIM>* p_node = rElement.GetNode(i);

            if (INTERPOLATION_LEVEL != CARDIAC) // don't interpolate X if cardiac problem
            {
                const c_vector<double, SPACE_DIM>& r_node_loc = p_node->rGetLocation();
                // interpolate x
                x.rGetLocation() += phi(i)*r_node_loc;
            }

            // interpolate u and grad u if a current solution or guess exists
            unsigned node_global_index = rElement.GetNodeGlobalIndex(i);
            if (mCurrentSolutionOrGuessReplicated.GetSize()>0)
            {
                for (unsigned index_of_unknown=0; index_of_unknown<(INTERPOLATION_LEVEL!=CARDIAC ? PROBLEM_DIM : 1); index_of_unknown++)
                {
                    // If we have a current solution (e.g. this is a dynamic problem)
                    // interpolate the value at this quad point

                    // NOTE - following assumes that, if say there are two unknowns u and v, they
                    // are stored in the current solution vector as
                    // [U1 V1 U2 V2 ... U_n V_n]
                    double u_at_node=GetCurrentSolutionOrGuessValue(node_global_index, index_of_unknown);
                    u(index_of_unknown) += phi(i)*u_at_node;

                    if (INTERPOLATION_LEVEL==NONLINEAR) // don't need to construct grad_phi or grad_u in other cases
                    {
                        for (unsigned j=0; j<SPACE_DIM; j++)
                        {
                            grad_u(index_of_unknown,j) += grad_phi(j,i)*u_at_node;
                        }
                    }
                }
            }

            // allow the concrete version of the assembler to interpolate any
            // desired quantities
            IncrementInterpolatedQuantities(phi(i), p_node);
        }

        double wJ = jacobian_determinant * mpQuadRule->GetWeight(quad_index);

        // create rAElem and rBElem
        if (mAssembleMatrix)
        {
            noalias(rAElem) += ComputeMatrixTerm(phi, grad_phi, x, u, grad_u, &rElement) * wJ;
        }

        if (mAssembleVector)
        {
            noalias(rBElem) += ComputeVectorTerm(phi, grad_phi, x, u, grad_u, &rElement) * wJ;
        }
    }
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeObjectAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AssembleOnSurfaceElement(
            const BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>& rSurfaceElement,
            c_vector<double, PROBLEM_DIM*ELEMENT_DIM>& rBSurfElem)
{
    c_vector<double, SPACE_DIM> weighted_direction;
    double jacobian_determinant;
    mpMesh->GetWeightedDirectionForBoundaryElement(rSurfaceElement.GetIndex(), weighted_direction, jacobian_determinant);

    rBSurfElem.clear();

    // allocate memory for the basis function values
    c_vector<double, ELEMENT_DIM>  phi;

    // loop over Gauss points
    for (unsigned quad_index=0; quad_index<mpSurfaceQuadRule->GetNumQuadPoints(); quad_index++)
    {
        const ChastePoint<ELEMENT_DIM-1>& quad_point = mpSurfaceQuadRule->rGetQuadPoint(quad_index);

        SurfaceBasisFunction::ComputeBasisFunctions(quad_point, phi);

        // interpolation

        // Location of the gauss point in the original element will be
        // stored in x
        ChastePoint<SPACE_DIM> x(0,0,0);

        this->ResetInterpolatedQuantities();
        for (unsigned i=0; i<rSurfaceElement.GetNumNodes(); i++)
        {
            const c_vector<double, SPACE_DIM> node_loc = rSurfaceElement.GetNode(i)->rGetLocation();
            x.rGetLocation() += phi(i)*node_loc;

            // allow the concrete version of the assembler to interpolate any
            // desired quantities
            IncrementInterpolatedQuantities(phi(i), rSurfaceElement.GetNode(i));
        }

        double wJ = jacobian_determinant * mpSurfaceQuadRule->GetWeight(quad_index);

        // create rAElem and rBElem
        noalias(rBSurfElem) += ComputeVectorSurfaceTerm(rSurfaceElement, phi, x) * wJ;
    }
}

#endif /*ABSTRACTFEOBJECTASSEMBLER_HPP_*/

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